The aim of this work is to solve hyperbolic conservation laws by means of a finite volume method for both spatial and time discretization. We extend the ideas developed in [X.-D. Liu and S. Osher, SIAM J. Numer. Anal., 33 (1996), pp. 760–779; X.-D. Liu and E. Tadmor, Numer. Math., 79 (1998), pp. 397–425] to fourth-order upwind and central schemes. In order to do this, once we know the cell-aver...

In this paper, we present a new metric to estimate the perceived difference in contrast between an original image and a reproduction. This metric, named weighted-level framework EE (WLF-DEE), implements a multilevel filtering based on the difference of Gaussians model proposed by Tadmor and Tolhurst (2000) and the new Euclidean color difference formula in log-compressed OSA-UCS space proposed b...

Many second order accurate non-oscillatory schemes are based on the Minmod limiter, for example the Nessyahu-Tadmor scheme. It is well known that the Lperror of monotone finite difference methods for the linear advection equation is of order 1/2 for initial data in W (Lp), 1 ≤ p ≤ ∞, see [2]. For a second or higher order non-oscillatory schemes very little is known because they are nonlinear ev...

We consider approximate solutions to nonlinear hyperbolic conservation laws. If the exact solution is unavailable, the truncation error may be the only quantitative measure for the quality of the approximation. We propose a new way of estimating the local truncation error, through the use of localized test-functions. In the convex scalar case, they can be converted into L∞loc estimates, followi...

We present a new formulation of three-dimensional central finite volume methods on unstructured staggered grids for solving systems of hyperbolic equations. Based on the Lax-Friedrichs and Nessyahu-Tadmor one-dimensional central finite difference schemes, the numerical methods we propose involve a staggered grids in order to avoid solving Riemann problems at cell interfaces. The cells are baryc...

In this paper, we consider several high-order schemes in one space dimension. In particular, we compare the second-order relaxation ( << 1) or “relaxed” ( = 0) schemes of Jin and Xin [Comm. Pure Appl. Math., 48 (1995), pp. 235–277] with the second-order Lax–Friedrichs scheme of Nessyahu and Tadmor [J. Comp. Phys., 87 (1990), pp. 408–463] and with higher-order essentially nonoscillatory (ENO) an...

Motivated by the hierarchical multiscale image representation of Tadmor et al., we propose a novel integrodifferential equation (IDE) for a multiscale image representation. To this end, one integrates in inverse scale space a succession of refined, recursive ‘slices’ of the image, which are balanced by a typical curvature term at the finer scale. Although the original motivation came from a var...

The article first studies the propagation of well prepared high frequency waves with small amplitude ε near constant solutions for entropy solutions of multidimensional nonlinear scalar conservation laws. Second, such oscillating solutions are used to highlight a conjecture of Lions, Perthame, Tadmor, ([23]), about the maximal regularizing effect for nonlinear conservation laws. For this purpos...